Find the median of the following data (rounded off to 2 decimal places):

| Class Interval | Frequency |
|----------------|-----------|
| 0-5 | 3 |
| 5-10 | 5 |
| 10-15 | 4 |
| 15-20 | 2 |
| 20-25 | 7 |
| 25-30 | 6 |
| 30-35 | 5 |

Question

Find the median of the following data (rounded off to 2 decimal places):

| Class Interval | Frequency |
|----------------|-----------|
| 0-5            | 3         |
| 5-10           | 5         |
| 10-15          | 4         |
| 15-20          | 2         |
| 20-25          | 7         |
| 25-30          | 6         |
| 30-35          | 5         |

Accepted Answer

**Solution:**

1. **Given data:**

| Class Interval | Frequency (f) |
|----------------|---------------|
| 0-5            | 3             |
| 5-10           | 5             |
| 10-15          | 4             |
| 15-20          | 2             |
| 20-25          | 7             |
| 25-30          | 6             |
| 30-35          | 5             |

2. **Calculate cumulative frequency (CF):**

| Class Interval | Frequency (f) | Cumulative Frequency (CF) |
|----------------|---------------|---------------------------|
| 0-5            | 3             | 3                         |
| 5-10           | 5             | 3 + 5 = 8                 |
| 10-15          | 4             | 8 + 4 = 12                |
| 15-20          | 2             | 12 + 2 = 14               |
| 20-25          | 7             | 14 + 7 = 21               |
| 25-30          | 6             | 21 + 6 = 27               |
| 30-35          | 5             | 27 + 5 = 32               |

3. **Total frequency (N) = 32**

4. **Find median class:**

- Median position = $\frac{N}{2} = \frac{32}{2} = 16$
- Locate the class where cumulative frequency just exceeds or equals 16.
- CF at 15-20 is 14 (less than 16), CF at 20-25 is 21 (greater than 16).
- So, median class = 20-25

5. **Identify values for median formula:**

- Lower boundary of median class, $l = 20$
- Frequency of median class, $f_m = 7$
- Cumulative frequency before median class, $CF = 14$
- Class width, $h = 5$

6. **Median formula:**

$$
	ext{Median} = l + \left( \frac{\frac{N}{2} - CF}{f_m} ight) 	imes h
$$

7. **Calculate median:**

$$
= 20 + \left( \frac{16 - 14}{7} ight) 	imes 5
= 20 + \left( \frac{2}{7} ight) 	imes 5
= 20 + \frac{10}{7}
= 20 + 1.4286 = 21.4286
$$

8. **Rounded to 2 decimal places:**

$$21.43$$

Answer

Answer

Answer